Analysis of Branched Cracks

1978 ◽  
Vol 45 (4) ◽  
pp. 797-802 ◽  
Author(s):  
K. K. Lo
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Complex Form ◽  
Function Technique ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Potential Formulation ◽  
Crack Problems

This paper presents a method for solving a class of two-dimensional elastic branched crack problems. In contrast to other approaches in the literature, the integral equation presented here enables different branched crack problems to be solved in a unified manner. Muskhelishvili’s potential formulation is used to derive, by means of a Green’s function technique, a singular integral equation in complex form. The problems of the asymmetrically, symmetrically, and doubly symmetrically branched cracks are considered. The ratio of the length of the branched crack to that of the main one may be varied arbitrarily and the limit in which this ratio goes to zero is obtained analytically. Stress-intensity factors at the branched crack tip are computed numerically and the results, where possible, are compared to those in the literature. Disagreements in the literature are discussed and clarified with the aid of the present results.

Interface Stress Analysis of the Bending Cylinder Containing Inclusion

2011 ◽  
Vol 201-203 ◽  
pp. 951-955
Author(s):  
Xin Yan Tang
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Stress Analysis ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Integral Equation Method ◽  
Equation Method ◽  
Intensity Factors ◽  
Engineering Structures

Using the elasticity and the singular integral equation method, an analysis of a bending cylinder containing inclusions is carried out. The disturbing interface stresses on the inclusion sides and the stress intensity factors at the inclusion tips are obtained. The results given in this paper are useful for the strength design of the engineering structures or mechanical components containing inclusions.

Transient Stress Intensity Factors of an Interfacial Crack Between Two Dissimilar Anisotropic Half-Spaces, Part 1: Orthotropic Materials

1984 ◽  
Vol 51 (1) ◽  
pp. 71-76 ◽  
Author(s):  
A.-Y. Kuo
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Jacobi Polynomials ◽  
Interfacial Crack ◽  
Orthotropic Materials ◽  
Intensity Factors ◽  
Orthotropic Solids

Transient response of an interfacial crack between two dissimilar elastic, orthotropic solids is investigated. The interfacial crack is excited by tractions suddenly applied on the crack surfaces. Governing equations, boundary conditions, and continuity conditions along the interface are reduced to a singular integral equation. Solution of the singular integral equation is obtained by the use of Jacobi polynomials. Expressions for stress intensity factors at the crack tip are given. As a sample problem, an interfacial crack in a 0 deg/90 deg fiber-reinforced composite solid excited by a suddenly applied uniform pressure on the crack surfaces is studied.

Transient Response of a Finite Bimaterial Plate Containing a Crack Perpendicular to and Terminating at the Interface

2005 ◽  
Vol 73 (4) ◽  
pp. 544-554 ◽  
Author(s):  
Xian-Fang Li ◽  
L. Roy Xu
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Transient Response ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Cauchy Kernel ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors

The transient response of a finite bimaterial plate with a crack perpendicular to and terminating at the interface is analyzed for two types of boundaries (free-free and clamped-clamped). The crack surface is loaded by arbitrary time-dependent antiplane shear impact. The mixed initial-boundary value problem is reduced to a singular integral equation of a generalized Cauchy kernel for the crack tearing displacement density or screw dislocation density. The Gauss-Jacobi quadrature technique is employed to numerically solve the singular integral equation, and then the dynamic stress intensity factors are determined by implementing a numerical inversion of the Laplace transform. As an example, numerical calculations are carried out for a cracked bimaterial plate composed of aluminum (material I) and epoxy or steel (material II). The effects of material properties, geometry, and boundary types on the variations of dynamic stress intensity factors are discussed in detail. Results indicate that an overshoot of the normalized stress intensity factor of the crack tip at the interface decreases for a cracked bimaterial plate, and the occurrence of which is delayed for a cracked aluminum/epoxy plate compared to a pure aluminum plate with the same crack.

The Linear Magnetoelastic Problem of Two Coplanar Griffith Cracks in a Soft Ferromagnetic Elastic Strip

1982 ◽  
Vol 49 (1) ◽  
pp. 69-74 ◽  
Author(s):  
Y. Shindo
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Fourier Transforms ◽  
Infinite Strip ◽  
Algebraic Equations ◽  
Intensity Factors ◽  
Soft Ferromagnetic

Following a linear theory for soft ferromagnetic elastic solids, we consider the problem of determining the stress-intensity factors in an infinite strip of a soft ferromagnetic elastic material containing two coplanar Griffith cracks. We assume that the solid is a homogeneous and isotropic one and it is permeated by a uniform magnetostatic field normal to the cracks surfaces and that the cracks are opened by a constant internal pressure. By the use of Fourier transforms we reduce the problem to that of solving two simultaneous triple integral equations. These equations are reduced to a singular integral equation of the first kind. By expanding the solution into the form of the product of the series of Chebyshev polynomials of the first kind and their weight function, the singular integral equation is further reduced to the infinite system of algebraic equations for the determination of the unknown coefficients. Numerical calculations are carried out and the influence of the magnetic fields on the stress-intensity factors is graphically shown in detail.

Boundary-Singular Integral Equation Method to Calculate the Bending Center and Stress Intensity Factors of Cracked Cylinder under Saint-Venant Bending

2007 ◽  
Vol 348-349 ◽  
pp. 197-200
Author(s):  
Xin Yan Tang
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Integral Equations ◽  
Cross Section ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Singular Integral Equations ◽  
Intensity Factors ◽  
Cracked Cylinder

Using single crack solution and regular plane harmonic function, the Saint-Venant bending problem of a cracked cylinder with general cross section is formulated in terms of two sets of boundary-singular integral equations, which can be solved by using the methods for combination of boundary element and singular integral equation methods. The concept of bending center used in strength of materials is extended to this bending problem. Theoretical formulae to calculate the bending center and stress intensity factors in cracked cylinder are derived and expressed by the solutions of the integral equations. Based on these results, some numerical examples are given for different configurations of the cylinder cross section as well as the crack parameters.

The Solution of Crack Problems by Using Distributed Strain Nuclei

1996 ◽  
Vol 210 (1) ◽  
pp. 23-31 ◽  
Author(s):  
A M Korsunsky ◽  
D A Hills
Keyword(s):  
Integral Equation ◽  
Stress Field ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Crack Problems ◽  
The Relationship ◽  
Distributed Strain

Crack problems may be solved by first establishing the stress field in the crack's absence and distributing strain nuclei along the line of the crack in order to render its faces traction-free. The relationship between the different possible forms of nucleus and the kinds of singular integral equation to which they lead are explored. The merits of each are then highlighted.

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